1. Making Measurements

2. SI system HW 1. A) g b) m. mm c) m 3 d) K e) m/s 2. A) 2g/cm 3 b) 25 kgm/s 2 (N) c. 13 m/s 2 3. A) 34000 mg b) 4.5 cm c) 120000 s d)0.0345 mole e) 65000 g

3. When you are doing the Measuring… Measurements ALWAYS have a number AND a unit You should never record a measurement without its unit! Record measurements one number past what is marked on the instrument. E.g. if it is marked every one degree then you should record to the tenths place by estimating the last number

5. 40.22 cm

6. Graduated Cylinder - Meniscus

8. 52.9 mL

9. Error in Measuring Uncertain Figure: the last number in a measurement that is an estimate. Measurements are understood to be + 1 in the uncertain figure.

10. Finding the volume of a regular shaped object. Measure the length. Measure the width. Measure the height. Multiply these together: L x W x H

11. Finding Volume of an Irregular Object Place water in the graduated cylinder. Record the water level. Sink the object into the water. Record the new water level. Subtract the two water levels. The answer is the volume. Change the mL to cm 3

12. Water Before: 30mL Water After: 40mL 40-30 =10 Difference is 10mL Object’s Volume: 10cm 3 What is the volume of this object?

13. Accuracy: measure of how close a measurement comes to the actual true value Precision: measure how close a series of measurements are to one another

14. Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

15. Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

16. Error Error = experimental –accepted value % Error= (|experimental –accepted|) x 100% accepted value PERCENT ERROR

17. Significant figures Any number that has meaning in a measurement. 1. Any nonzero number is significant. Ex: 198 2. Zeros between two significant numbers are significant. Ex: 409 3. Initial zeros, before nonzero numbers are not significant. Ex: 0.00894 4. Final zeros after nonzero numbers which have a decimal are significant. Ex: 38.50 5. Final zeros without a decimal are not significant. Ex: 4500

18. How many significant figures are in each of the following? 1) 0.00987 2) 0.00540 3) 6.70 x 10 -5 4) 1.0 5) 12.87 6) 6700000 7) 30.000 8) 0.098

19. Calculations with measurements Calculations do not make measurements more accurate!!!

20. Exact numbers Exact numbers have as many significant figures as needed They do not affect calculations. Examples of exact numbers: Counting numbers (There are 32 people in this class) Definitions (1m = 100cm, 60min = 1 hr)

21. Rounding calculations done with measurements It is the calculators job to do the math… It is your job to round numbers off to the correct number of significant figures!!!!

22. Addition and Subtraction Answers have the same number of decimal places as the measurement with the least number. 10.8 m + 1.32 m

23. Multiplication and Division The answer has the same number of significant figures as the measurement with the least. (4.78 cm)(0.90 cm)(0.08cm) =

24. 1. 127.890 + 10.09 137.98 2. 0.7898 - 0.089 0.7008 3. 140.0 X 90.90 12726 4. 0.000097 X 0.000323 3.1331 x 10 -8 5. 42.99___ 0.00343 6. 345.18 x 120.00 231.230 = 179.1359253 = 12533.5277

25. Answers 1.137.98 (2 decimal places) 2.0.701 (3 decimal places) 3.12730 (4 significant digits--since there is no decimal the zero at the end is not significant) 4.3.1 x 10-8 (2 significant digits—trailing zeros are not significant) 5.12500 (3 significant digits—trailing zeros are not significant) 6.179.14 (5 significant digits)